I may have just registered on a forum to post on a thread thats not been used in a year and eight months I've been thinking about this myself (quite unaware it'd ever crossed anyone elses mind)
SOme of the posters in these threads have had some genius ideas to cram all sorts of extra units into an arbites force, but to be honest they're not quite how I envisioned it. The way I always looked at Arbites is hat they couldn't and really shouldn't be made into balanced army that stood a chance against a proper field army. They are after all only a smaller scale organization to be used to suppress rebellion and rioting. I thought they would be best used in small 'combat patrol games' and games with a heavy narrative where their enemies forces were prescribed specifically to give them a chance.
My plans were only to use units that are games workshop cannon for arbites/enforcers. If my background knowledge is right (and as I neither played in the 80's nor have read all the BL books, it could be well out) the only units Arbites have even been given is patrolmen squads, cybermstifs, judges as leaders and mounted in repressors (the IA2 book that introduces repressors states that the sisters of battle adopted them after working with the arbites).
A 'legal' army could thus quite easily be made with very little 'counts as'. As Khemri noted in another thread the WH Stormtrooper is also intended for use as arbites. Repressors are intended as a FW addition to the WH list so fielding them would be fine. Some small proxying would then be necessary to have Arbite Judges count as the two ranks of inquisitor (with a retinue of more arbites as stormtroopers are an option) and something to represent the mastiffs, possibly archo flagellants. If there has been mention of Arbites using a Leman Russ in a novel as Ambience suggests, then that could easily be used as inducted guard.
Before I'd read this thread I was also considering inducted conscripts as penal legion troops (I know there is a penal legion entry in the IG book, but I always figured that would represent courtmarshelled military type with training and experience, not the hive gangers and street scum that would be in the arbites gaols). However as some people have pointed out, using prisoners as soldiers may not be that much in character and not many criminals would be lucky enough to end up as prisoners (and I'm not sure would be legal without a guard platoon first).
This whole lot could be represented by a load of necromnda enforcer box sets and some forgeworld purchases, and if you could get some old arbites minis off ebay to add some variety and provide the HQ units all the better.
Now I know this would give one a very limited army, with few choices and almost no ability to face heavy infantry or enemy armor, to me this would seem in character. They should be fighting small scale skirmishes in the streets and fighting chaos cultists, rogue governors palace guards and genestealer cults etc. If some sort of invasion, daemon incursion or major military rebellion occurred the arbites, if I understand the fluff correctly, would have to defer to the planetary defense forces or IG garrisons (and could be nicely represented as allies to a Codex: IG army). If they did end up facing those on their own (as they do in a number of books) they would almost certainly, after putting up a stiff fight, die (as they do in the books).